Maxfield's result follows immediately - via the pointwise ergodic theorem - from the ergodicity of the measure preserving transformation \(T_{b_1} \times \cdots \times T_{b_s}\)  acting on \([0,1]^s\) . On the other hand, formula (REF ) (and even its special case (REF )) is quite a bit less trivial and manifests a subtle “diagonal phenomenon" which is also behind Furstenberg's approach to Szemerédi's theorem (see [1]}).

